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The answer depends on the exact definition of the set of fundamental constants, as well as on the choice of base units of a given system of units. A look at the NIST page Fundamental Physical Constants --- Complete Listing shows that they list too many fundamental constants to allow assignment of a unit value to each of them, within the International ...

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You can use "natural units" to set some of the fundamental constants (usually $\hbar$, $c$, Coulomb's constant) equal to one, but this fixes the values of other constants as values other than one. For example, by setting $\hbar$, $c$ and $k_e$ equal to one, you can find the elementary charge, $e$, in terms of the fine structure constant, $\alpha$. \alpha=...

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Everything!!! Natural units just make your life simpler, is like removing every unnecessary conversion factors which need to be added, helps by making the equation look smaller, and can easily give back the final equation just by dimensional analysis. Okay you might be wondering what dimensional analysis has got to do with natural units. Well let's see an ...

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